Power creep refers to new characters getting stronger over time, leaving older characters somewhat in the dust. A power creep can be due to a variety of things, but the most common reason is likely innovation. With new, better character creation, you get new, better characters. This tends to leave older characters out in the cold. This may lead to buffs for older characters.

The power creep in top lane is a bit of the same, though on a micro level. This refers to power within a single game. Top lane, more than others, tends to snowball because there is more 1v1 fighting and less help from the team (as there are no large objectives near top lane apart from towers). If one person gains even a small advantage in top lane, the advantage tends to grow and grow because one player is stronger and therefore can deny, kill, or out CS her opponent.

For some reason I remember hearing it like, "whoever wins the power creep" when referring to top lane.

People usually refer to top when they talk about power creep because it's been by far the most apparent up there. Top lane is the harshest lane in terms of match-ups and champions made to be sent up there are purposefully made to have a strong laning phase that generally drops off later. Riven was the shining example of this happening, but in the last few months the whole thing has become even more apparent with Darius, Rengar, and Jayce being released.